Flexible band types of wrenches have been known in the art for a great many years although they have not been extensively used except for the removal of oil filters. The ranges of adjustment of such wrenches have been relatively limited and in most cases the wrenches have been expensive to manufacture. Since, however, flexible band wrenches have two important advantages over the more customary wrenches, i.e., they do not gouge or mar the workpiece and they are adaptable to various shapes of workpieces, it would be desirable to provide an adjustable flexible band wrench which would be easy to adjust and which would be adjustable within a wide range of sizes.